A polynomial function is a mathematical expression that involves variables raised to whole number powers, combined using addition, subtraction, and multiplication. The general form of a polynomial function in one variable is f(x) = a_n x^n + a_n-1 x^n-1 + \ldots + a_1 x + a_0 , where a_n, a_n-1, \ldots, a_0 are constants, and n is a non-negative integer representing the degree of the polynomial. Polynomial functions can have various shapes and behaviors depending on their degree and coefficients. They are widely used in fields such as algebra, calculus, and engineering to model real-world situations. The degree of the polynomial determines the number of roots it can have, which are the values of x where the function equals zero.